\documentclass{standalone}
\usepackage{tikz} % Required for drawings
\usetikzlibrary{positioning} % Required for node positioning, e.g. 'above right=of'
\usepackage{helvet}
\usepackage[eulergreek]{sansmath}

\begin{document}
	\tikzstyle{node}=[draw,circle,minimum size=0.8cm,node distance=1.5cm,font=\sansmath\sffamily]
	\tikzstyle{label}=[font=\small\sansmath\sffamily,inner sep=1pt]
	\tikzstyle{edge}=[-latex]
	\tikzstyle{route}=[line width=2.5pt,red,opacity=0.6]

	\begin{tikzpicture}
		\node [node] (0) {0};
		\node [node, above right=of 0] (1) {1};
		\node [node, below right=of 0] (2) {2};
		\node [node, right=of 1] (3) {3};
		\node [node, right=of 2] (4) {4};
		\node [node, below right=of 3] (5) {5};

		\draw[edge] (0.30) to node[label,below right] {(0,3)} (1.-120);
		\draw[edge] (1.-150) to node[label,above left] {(1,3)} (0.60);
		\draw[edge] (0) to node[label,above right] {(2,4)} (2);
		\draw[edge] (3) to node[label,above] {(3,4)} (1);
		\draw[edge] (1.-70) to node[label,below left] {(4,2)} (4.140);
		\draw[edge] (4.110) to node[pos=0.75,label,above right] {(5,2)} (1.-40);
		\draw[edge] (2) to node[label,above] {(6,6)} (4);
		\draw[edge] (3.-105) to node[pos=0.3,label,left] {(7,4)} (4.105);
		\draw[edge] (4.75) to node[label,right] {(8,4)} (3.-75);
		\draw[edge] (3) to node[label,above right] {(9,3)} (5);
		\draw[edge] (5) to node[label,below right] {(10,3)} (4);

		\draw[route,shorten <={3 * 0.14cm}] (0.30) to (1.-120);
		\draw[route] (1.-70) to (4.140);
		\draw[route] (4.75) to (3.-75);
		\draw[route,shorten >={3 * 0.14cm}] (3) to (5);
	\end{tikzpicture}
\end{document}
